Method and apparatus for correcting distortion

ABSTRACT

A method and apparatus for correcting a distortion are provided. The distortion correction method includes displaying a first image on a display panel based on source images that correspond to respective viewpoints of the display panel, generating a second image by capturing the display panel at a first point, and determining a first compensation value to be used to compensate for a distortion of the second image with respect to the display panel.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims priority from Korean Patent Application No.10-2016-0152787, filed on Nov. 16, 2016, in the Korean IntellectualProperty Office, the disclosure of which is incorporated herein byreference in its entirety.

BACKGROUND 1. Field

Methods and apparatuses consistent with exemplary embodiments relate toa distortion correction method of a three-dimensional (3D) imagingapparatus and an apparatus that implements the distortion correctionmethod.

2. Description of the Related Art

The most dominant factor for recognizing stereoscopic images is adifference between images shown to both eyes of a user. A scheme ofdisplaying different images to both eyes of a user includes, forexample, a glasses scheme of filtering a desired image by a divisionusing polarized light, a time division or a wavelength division usingdifferent wavelengths of a primary color, and a glasses-free scheme ofenabling each image to be viewed in a predetermined space by using athree-dimensional (3D) conversion apparatus, for example, a parallaxbarrier, a lenticular lens or a directional backlight unit (BLU). Theglasses-free scheme may reduce an inconvenience of wearing glasses.However, when an error which is different from a design value occurs ina production process of a 3D display apparatus or a process ofinstalling a 3D conversion apparatus, an image quality may be degradeddue to crosstalk.

SUMMARY

Exemplary embodiments may address at least the above problems and/ordisadvantages and other disadvantages not described above. Also, theexemplary embodiments are not required to overcome the disadvantagesdescribed above, and an exemplary embodiment may not overcome any of theproblems described above.

According to an aspect of an exemplary embodiment, there is provided adistortion correction method including assigning viewpoints to pixels ofa display panel, displaying a first image on the display panel based onsource images that correspond to the viewpoints, generating a secondimage based on an image acquired by capturing the display panel at afirst point while the first image is output via a three-dimensional (3D)optical apparatus, determining a first compensation value that is usableto compensate for a distortion of the second image due to a geometricdistortion between the display panel and the 3D optical apparatus, andupdating at least one of the viewpoints based on the first compensationvalue.

The determining of the first compensation value may include determiningthe first compensation value based on a difference between the secondimage and a source image that corresponds to a viewpoint of the firstpoint. The distortion correction method may further include determininga reference source image observed at a reference point in the secondimage. The determining of the first compensation value may includedetermining the first compensation value so that the reference sourceimage is displayed on an entire area of the second image. The sourceimages may have respective feature values that correspond to viewpointnumbers. The determining of the first compensation value may includedetermining the first compensation value based on a difference between afeature value of the reference source image and at least one featurevalue of the other source images. The source images may have respectivefeature values determined based on hue values that are at regularintervals or intensity values that are at regular intervals.

The distortion correction method may further include determining asecond compensation value based on a third image generated by capturingthe display panel at a second point, the second compensation value beingusable to compensate for a distortion of the third image, anddetermining a third compensation value based on the first compensationvalue and the second compensation value, the third compensation valuebeing usable to compensate for a distortion observed at a third point.The updating of at least one of the viewpoints may include updating atleast one of the viewpoints based on the third compensation value. Thethird compensation value may be determined based on a distance betweenthe first point and the second point and a difference between the firstcompensation value and the second compensation value. The distortioncorrection method may further include detecting an eye position of auser of the display panel, and determining the third point based on thedetected eye position.

The distortion correction method may further include determiningrespective fields of view (FOVs) for each of the pixels based on ageometric model of the 3D optical apparatus, determining respectiveangles formed by the first point, each of the pixels and a fourth pointthat is different from the first point, determining an adjustment valuebased on the FOVs and the angles, the adjustment value being usable tocompensate for a distortion observed at the fourth point, and updatingat least one of the viewpoints based on the adjustment value. Thegeometric model may be determined based on a gap between the displaypanel and the 3D optical apparatus, and the gap may be estimated basedon the first compensation value. The adjustment value may be determinedbased on a ratio between the FOVs and the angles.

According to another aspect of an exemplary embodiment, there isprovided a distortion correction method including assigning viewpointsto pixels of a display panel, displaying a first image on the displaypanel based on source images that correspond to the viewpoints,generating a second image and a third image based on respective imagesacquired by capturing the display panel at a first point and a secondpoint while the first image is output via a 3D optical apparatus,determining a first compensation value that is usable to compensate fora distortion of the second image and a second compensation value that isusable to compensate for a distortion of the third image, determining athird compensation value based on the first compensation value and thesecond compensation value, the third compensation value being usable tocompensate for a distortion observed at a third point, and updating atleast one of the viewpoints based on the third compensation value.

According to another aspect of an exemplary embodiment, there isprovided a distortion correction method including assigning viewpointsto pixels of a display panel, displaying a first image on the displaypanel based on source images that correspond to the viewpoints,generating second images based on respective images acquired bycapturing the display panel at corresponding capturing points while thefirst image is output via a 3D optical apparatus, determining, based onthe generated second images, visible pixel lines associated with visiblepixels of the display panel observed at the capturing points,determining intersection points between the visible pixel lines and aline that corresponds to a viewing position, and reassigning a viewpointthat corresponds to the viewing position to pixels that corresponds tothe determined intersection points among the pixels of the displaypanel.

The determining of the visible pixel lines may include determiningcorresponding points for the visible pixels based on respective pixelvalues of the generated second images, the corresponding pointsrepresenting respective positions of the visible pixels based on thecapturing points, and determining the visible pixel lines by connectingthe determined corresponding points. The source images may haverespective feature values that correspond to viewpoint numbers. Thedetermining of the corresponding points may include determining a pixelof the display panel that corresponds to a first pixel included in thefirst image as a visible pixel, based on a comparison between a featurevalue of the first pixel and a feature value of a second pixel thatcorresponds to the first pixel among pixels included in the generatedsecond images, and determining a corresponding point for the visiblepixel based on the feature value of the second pixel.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other aspects of exemplary embodiments will becomeapparent and more readily appreciated from the following detaileddescription of certain exemplary embodiments, taken in conjunction withthe accompanying drawings of which:

FIG. 1 is a diagram illustrating a distortion correction system,according to an exemplary embodiment;

FIG. 2 is a diagram illustrating assignment of viewpoints, according toan exemplary embodiment;

FIG. 3 is a diagram illustrating feature values, according to anexemplary embodiment;

FIG. 4 is a flowchart illustrating a process of determining acompensation value, according to an exemplary embodiment;

FIG. 5 is a diagram illustrating an example of a viewpoint compensationprocess based on a compensation value, according to an exemplaryembodiment;

FIG. 6 is a diagram illustrating another example of a viewpointcompensation process based on a compensation value, according to anexemplary embodiment;

FIG. 7 is a diagram illustrating a process of estimating a gap,according to an exemplary embodiment;

FIG. 8 is a diagram illustrating a process of determining an adjustmentvalue, according to an exemplary embodiment;

FIG. 9 is a diagram illustrating a viewpoint adjustment process based onan adjustment value, according to an exemplary embodiment;

FIG. 10 is a diagram illustrating a process of determining correspondingpoints for visible pixels, according to an exemplary embodiment;

FIG. 11 is a diagram illustrating a relationship between a gap andvisible pixel lines, according to an exemplary embodiment;

FIG. 12 is a diagram illustrating visible pixel lines and a line,according to an exemplary embodiment;

FIG. 13 is a diagram illustrating observation of feature values,according to an exemplary embodiment;

FIG. 14 is a diagram illustrating a process of determining a visiblepixel, according to an exemplary embodiment;

FIG. 15 is a diagram illustrating correction of a head-up display (HUD)image, according to an exemplary embodiment;

FIG. 16 is a diagram illustrating correction of an image of smartglasses, according to an exemplary embodiment;

FIG. 17 is a block diagram illustrating a distortion correctionapparatus, according to an exemplary embodiment;

FIG. 18 is a flowchart illustrating an example of a distortioncorrection method, according to an exemplary embodiment; and

FIG. 19 is a flowchart illustrating another example of a distortioncorrection method, according to an exemplary embodiment.

DETAILED DESCRIPTION

The following structural or functional descriptions are exemplary tomerely describe the exemplary embodiments, and the scope of theexemplary embodiments is not limited to the descriptions provided in thepresent specification. Various changes and modifications can be madethereto by those of ordinary skill in the art.

Although terms of “first” or “second” are used to explain variouscomponents, the components are not limited to the terms. These termsshould be used only to distinguish one component from another component.For example, a “first” component may be referred to as a “second”component, or similarly, and the “second” component may be referred toas the “first” component within the scope of the right according to theconcept of the present disclosure.

As used herein, the singular forms are intended to include the pluralforms as well, unless the context clearly indicates otherwise. It shouldbe further understood that the terms “comprises” and/or “comprising,”when used in this specification, specify the presence of statedfeatures, integers, steps, operations, elements, components or acombination thereof, but do not preclude the presence or addition of oneor more other features, integers, steps, operations, elements,components, and/or groups thereof.

Unless otherwise defined herein, all terms used herein includingtechnical or scientific terms have the same meanings as those generallyunderstood by one of ordinary skill in the art. Terms defined indictionaries generally used should be construed to have meaningsmatching with contextual meanings in the related art and are not to beconstrued as an ideal or excessively formal meaning unless otherwisedefined herein.

Hereinafter, exemplary embodiments will be described in detail withreference to the accompanying drawings, and like reference numerals inthe drawings refer to like elements throughout.

FIG. 1 is a diagram illustrating a distortion correction system 100,according to an exemplary embodiment. Referring to FIG. 1, thedistortion correction system 100 includes a distortion correctionapparatus 110, a display panel 120, a three-dimensional (3D) opticalapparatus 130 and cameras 140, 150 and 160. The display panel 120 andthe 3D optical apparatus 130 may jointly constitute a glasses-freethree-dimensional (3D) display apparatus. The glasses-free 3D displayapparatus may be used to enable a user to view a 3D image even thoughthe user does not wear an additional device, such as, for example,glasses. Light output from each of pixels included in a display panel ofa two-dimensional (2D) display apparatus may propagate in alldirections, whereas light may be output from each of pixels included inthe display panel 120 of the glasses-free 3D display apparatus in adirection that is limited by the 3D optical apparatus 130. Accordingly,different respective images may be incident on both eyes of a user, andthe user may feel a 3D effect.

In the glasses-free 3D display apparatus, the 3D optical apparatus 130may be attached onto a front surface or a rear surface of a panel. The3D optical apparatus 130 may control a traveling direction of light thatpropagates through a panel. The display panel 120 may include, forexample, a liquid crystal display (LCD) panel, a light emitting diode(LED) panel, or an organic light emitting diode (OLED) panel. The 3Doptical apparatus 130 may include, for example, a lens array, a parallaxbarrier, or a directional backlight unit (BLU). For example, pixels ofthe display panel 120 may output light in all directions. When the 3Doptical apparatus 130 is a lens array, light may be refracted by thelens array and may be output in a predetermined direction only. When the3D optical apparatus 130 is a parallax barrier, light that propagates ina predetermined direction may be allowed to pass through the parallaxbarrier, and light that propagates in the other directions may beblocked.

In a process of manufacturing the 3D optical apparatus 130, the 3Doptical apparatus 130 may have parameters other than a predesignedparameter. Parameters may include, for example, a pitch that indicates aperiodicity of a lens or a barrier, a slanted angle that indicates adegree to which a lens or a barrier is inclined, a gap that indicates adistance between the display panel 120 and a lens or a barrier, and anoffset that indicates an x-axis relationship between the display panel120 and a lens or a barrier. When a 3D image is output based on apredesigned parameter instead of parameters of the 3D optical apparatus130 that is actually manufactured, crosstalk may occur, or the 3D imagemay be distorted. When the crosstalk occurs, a user may view a blurredimage or a distorted image that causes dizziness when a severe erroroccurs.

To prevent the crosstalk, a scheme of estimating a parameter for actualviewing and of generating a 3D image based on the estimated parametermay be used. To estimate the parameter, a 3D optical apparatus may needto be defined by the parameter. A parameter estimation scheme may beapplicable to a structure that may be represented by parameters.Accordingly, it may be difficult to apply the parameter estimationscheme to a 3D optical apparatus that is partially bent or partiallydistorted, or that has a shape that makes it difficult to perform apolynomial approximation. Further, because estimating of a parameter inthe parameter estimation scheme is dependent on parameters, a 3D opticalapparatus with a shape that may not be represented by parameters may notbe corrected using the parameter estimation scheme.

To correct a distortion, the distortion correction apparatus 110 maydirectly assign compensation values for all pixels, instead ofapproximating a geometric shape by using parameters. Accordingly, adistortion of a 3D optical apparatus that is partially bent or distortedor that has an atypical shape may be corrected. For example, thedistortion correction apparatus 110 may assign viewpoints to pixels ofthe display panel 120 based on a predetermined rule, and may display afirst image on the display panel 120 based on respective source imagesthat correspond to the viewpoints. The distortion correction apparatus110 may output the first image via the 3D optical apparatus 130 byproviding light to the display panel 120. The camera 160 may capture thedisplay panel 120 at a first point 165 while the first image is outputvia the 3D optical apparatus 130. The capturing of the display panel 120may include capturing the glasses-free 3D display apparatus whichincludes the display panel 120 and the 3D optical apparatus 130. Thedistortion correction apparatus 110 may generate a second image based onan image acquired by the camera 160. The second image may be an imagethat is converted to correspond to the first image, and the distortioncorrection apparatus 110 may cut or rotate the image acquired by thecamera 160, in order to generate the second image.

The display panel 120 or the 3D optical apparatus 130 may be partiallybent or partially distorted. Based on the above shape, a geometricdistortion may occur between the display panel 120 and the 3D opticalapparatus 130, and the second image may include a distortion by thedisplay panel 120 and the 3D optical apparatus 130. The distortioncorrection apparatus 110 may determine a compensation value that isusable to compensate for a distortion of the second image. For example,the distortion correction apparatus 110 may determine a compensationvalue based on a difference between the second image and a source imagethat corresponds to a viewpoint of the first point 165. A process ofdetermining a compensation value will be further described below. Thedistortion correction apparatus 110 may compensate for the distortion ofthe second image based on the determined compensation value by updatingat least one or several of the viewpoints assigned to the pixels.

The compensation value determined based on the first point 165 may belimited in correction of a distortion observed at a third point 175. Inan example, in order to correct the distortion observed at the thirdpoint 175, an additional compensation value based on the camera 150 maybe used. Similarly to the camera 160, the camera 150 may capture thedisplay panel 120 at a second point 155 while the first image is outputvia the 3D optical apparatus 130. The distortion correction apparatus110 may generate a third image based on the image acquired by the camera160, and may determine a compensation value that is usable to compensatefor a distortion of the third image. The distortion correction apparatus110 may estimate a compensation value of the third point 175 based onthe compensation values that correspond to the first point 165 and thesecond point 155. The estimated compensation value may be used tocorrect a distortion observed by a user located at the third point 175.The distortion correction apparatus 110 may store the compensationvalues that correspond to the first point 165 and the second point 155in a manufacturing process, and may estimate a compensation value basedon a position of a user based on the compensation values that correspondto the first point 165 and the second point 155 in an actual useprocess. The distortion correction apparatus 110 may track a position ofa user that is using the camera 140.

In another example, an adjustment value may be used to correct adistortion observed by a user at the third point 175. The distortioncorrection apparatus 110 may determine a geometric model of the 3Doptical apparatus 130 based on a compensation value, and may determinean adjustment value for the third point 175 based on the geometricmodel. In this example, the compensation value may be determined basedon an image acquired by a single camera, for example, the camera 160.The distortion correction apparatus 110 may estimate a gap between thedisplay panel 120 and the 3D optical apparatus 130 based on thecompensation value, and may determine the geometric model based on theestimated gap. A process of determining an adjustment value will befurther described below. The distortion correction apparatus 110 maydetermine a compensation value based on an image captured at a point,for example, the first point 165, and may determine the geometric modelbased on the compensation value, in order to acquire an adjustment valuefor another point, for example, the third point 175.

The 3D optical apparatus 130 may have an atypical shape, for example, acurve, that may not be represented by parameters. Because a compensationvalue is determined independently of a parameter of the 3D opticalapparatus 130, the distortion correction apparatus 110 may compensatefor a distortion of the 3D optical apparatus 130 based on thecompensation value regardless of a shape of the 3D optical apparatus130. For example, when the 3D optical apparatus 130 is partially bent orpartially distorted, and when the 3D optical apparatus 130 has a shapethat makes it difficult to perform a polynomial approximation, forexample, a front glass of a vehicle or a lens of glasses, the distortioncorrection apparatus 110 may compensate for the distortion of the 3Doptical apparatus 130.

The distortion correction apparatus 110 may generate an image with acorrected distortion by assigning viewpoint numbers to all the pixels ofthe display panel 120 based on Equation 1 shown below.

v _(ij) =v _(ij) ^(a) +v _(ij) ^(c) +v _(ij) ^(w)  [Equation 1]

In Equation 1, v_(ij) denotes a viewpoint number of a pixel thatcorresponds to an i-th row and j-th column, v_(ij) ^(a) denotes aninitial viewpoint number of the pixel that corresponds to the i-th rowand j-th column, v_(ij) ^(c) denotes a compensation value for the pixelthat corresponds to the i-th row and j-th column, and v_(ij) ^(w)denotes an adjustment value for the pixel that corresponds to the i-throw and j-th column. The compensation value v_(ij) ^(c) may beassociated with a fixed point, for example, the first point 165, and maybe used for a user who observes an image at the fixed point. Inaddition, compensation values determined for a plurality of points, forexample, the first point 165 and the second point 155, may be used todetermine a compensation value for another point, for example, the thirdpoint 175. To determine the compensation value for the other point, theadjustment value v_(ij) ^(w) may be additionally used.

FIG. 2 is a diagram illustrating assignment of viewpoints, according toan exemplary embodiment. FIG. 2 illustrates a display panel 210 and a 3Doptical apparatus 220. The display panel 210 may include a plurality ofpixels, and various parameters associated with the 3D optical apparatus220 or a relationship between the display panel 210 and the 3D opticalapparatus 220 may be defined. Parameters may include, for example, apitch that indicates a periodicity of a lens or a barrier, a slantedangle that indicates a degree to which a lens or a barrier is inclined,a gap that indicates a distance between a display panel and a lens or abarrier, and an offset that indicates an x-axis relationship between adisplay panel and a lens or a barrier.

A distortion correction apparatus may assign initial viewpoint numbersto all the pixels of the display panel 210. For example, the distortioncorrection apparatus may assign the initial viewpoint numbers by usingEquation 2 shown below.

$\begin{matrix}{v_{ij}^{a} = {N \times {{mod}\left( {{\frac{j - f - {i\; \tan \; \alpha}}{p\; \cos \; \alpha}\frac{d - t}{d}},{p\; \cos \; \alpha \frac{d}{d - t}}} \right)}}} & \left\lbrack {{Equation}\mspace{14mu} 2} \right\rbrack\end{matrix}$

In Equation 2, v_(ij) ^(a) denotes an initial viewpoint number of apixel that corresponds to an i-th row and j-th column, N denotes a totalnumber of viewpoints, i denotes a row of a pixel, and j denotes a columnof a pixel. Also, f denotes an offset, α denotes a slanted angle, pdenotes a pitch, d denotes a distance between the display panel 210 anda camera, and t denotes a gap.

FIG. 3 is a diagram illustrating feature values, according to anexemplary embodiment. In a distortion correction process, feature valuesmay be used. A distortion correction apparatus may assign feature valuesto viewpoint numbers, and may calculate a compensation value or anadjustment value based on the feature values. As described above, afirst image may be generated based on source images. The first image mayhave a plurality of viewpoints, and different source images may beapplied for each of the viewpoints of the first image. The source imagesmay have different feature values based on viewpoints. The featurevalues may be determined based on hue values that are at regularintervals, and/or based on intensity values that are at regularintervals. An intensity may refer to an intensity of light. Based on thefirst image generated based on the source images with the featurevalues, a distortion may be intuitively observed and easily corrected.In the following description, a hue value will be described as anexample, however, there is not limitation thereto. Accordingly, thefollowing description may also be applicable to an intensity and anotherexample.

The distortion correction apparatus may divide the feature values basedon the total number N of viewpoints, so that the feature values assignedto the viewpoint numbers may be at regular intervals. For example, whena range M of hue values is set to “360” and the total number N ofviewpoints is set to “10,” a hue value of “0” may be assigned to a firstviewpoint, a hue value of “36” may be assigned to a second viewpoint,and a hue value of “324” may be assigned to a tenth viewpoint. In thisexample, a red image that corresponds to the hue value of “0” may needto be observed at a point that corresponds to the first viewpoint. Whenan image that includes another color is observed at the point thatcorresponds to the first viewpoint, the image may include a distortion,and accordingly the distortion may be corrected by the hue value.Because the feature values are assigned to the viewpoints at regularintervals, a linear transformation between the viewpoints may beperformed based on the feature values. Accordingly, a compensation valueor an adjustment value may be easily calculated based on a lineartransformation between the viewpoints, which will be further describedbelow.

FIG. 4 is a flowchart illustrating a process of determining acompensation value, according to an exemplary embodiment. Referring toFIG. 4, in operation 410, a distortion correction apparatus initializesa compensation value v_(ij) ^(c). The distortion correction apparatusmay initialize the compensation value v_(ij) ^(c) to zero. In operation420, the distortion correction apparatus generates a first image R_(ij)^(m) based on source images. The distortion correction apparatus maygenerate the first image R_(ij) ^(m) based on Equation 3 shown below.

R _(ij) ^(m) =v _(ij) ^(a) +v _(ij) ^(c)  [Equation 3]

In Equation 3, m denotes a number of repetitions. Referring to Equation3, the first image R_(ij) ^(m) may be determined based on an initialviewpoint number v_(ij) ^(a) and the compensation value v_(ij) ^(c).Because the compensation value v_(ij) ^(c) continues to be updated, thefirst image R_(ij) ^(m) may also continue to be updated until thecompensation value v_(ij) ^(c) converges to a predetermined level, whichwill be further described below. As described above, the distortioncorrection apparatus may assign hue values to viewpoints.

In operation 430, the distortion correction apparatus generates a secondimage C_(ij) ^(m) based on an image acquired by capturing a displaypanel. The second C_(ij) ^(m) image may be an image obtained byconverting the acquired image so as to correspond to the first imageR_(ij) ^(m). For example, the distortion correction apparatus may cut orrotate the image acquired by capturing the display panel, in order togenerate the second image C_(ij) ^(m). In operation 440, the distortioncorrection apparatus analyzes the second image C_(ij) ^(m). For example,when hue values are assigned to viewpoints and when various colors areincluded in the second image C_(ij) ^(m), the second image C_(ij) ^(m)may be determined to be distorted. The distortion correction apparatusmay determine an appropriate compensation value v_(ij) ^(c) so that asingle color may be included in the second image C_(ij) ^(m).

The distortion correction apparatus may determine a reference point inthe second image C_(ij) ^(m). An image observed at the reference pointmay be referred to as a “reference source image.” For example, thedistortion correction apparatus may determine the compensation valuev_(ij) ^(c) so that the reference source image may be displayed on anentire area of the second image C_(ij) ^(m). The reference point may be,for example, a central point of the second image C_(ij) ^(m) or a pointthat is perpendicularly oriented with respect to a camera that capturesthe display panel in the second image C_(ij) ^(m). When a hue value atthe reference point is defined as h₀ ^(m), a difference between the huevalue h₀ ^(m) and hue values of all the pixels of the second imageC_(ij) ^(m) may be obtained by using Equation 4 shown below.

Δh _(ij) ^(m) =h ₀ ^(m) −h _(ij) ^(m)  [Equation 4]

In Equation 4, h_(ij) ^(m) denotes a hue value of a pixel thatcorresponds to an i-th row and j-th column, and Δh_(ij) ^(m) denotes adifference between the hue value h_(ij) ^(m) and the hue value h₀ ^(m).Based on Equation 4, the compensation value v_(ij) ^(c) may berepresented as expressed in Equation 5 below.

$\begin{matrix}{v_{ij}^{c} = {\sum\limits_{m = 1}^{M}\left( {\frac{\Delta \; h_{ij}^{m}}{360}N} \right)}} & \left\lbrack {{Equation}\mspace{14mu} 5} \right\rbrack\end{matrix}$

In Equation 5, 360 denotes a range of hue values. The range of the huevalues may be defined by another number, depending on exemplaryembodiments.

In operation 450, the distortion correction apparatus updates thecompensation value v_(ij) ^(c). In operation 460, the distortioncorrection apparatus determines whether the compensation value v_(ij)^(c) converges. When the compensation value v_(ij) ^(c) does notconverge, the distortion correction apparatus may repeat operation 420.When the number of repetition increases, hue values of the second imageC_(ij) ^(m) may converge to the hue value h₀ ^(m). When the compensationvalue v_(ij) ^(c) converges, the distortion correction apparatus mayproceed to operation 470. When a variance of hue values is less than orequal to a predetermined threshold, the distortion correction apparatusmay determine that the compensation value v_(ij) ^(c) converges. Inoperation 470, the distortion correction apparatus determines thecompensation value v_(ij) ^(c) that converges. The compensation valuev_(ij) ^(c) may be determined at a single point or at a plurality ofpoints. The distortion correction apparatus may determine compensationvalues v_(ij) ^(c) for each of the plurality of points by performingoperations 410 through 470 for each of the plurality of points.

FIG. 5 is a diagram illustrating an example of a viewpoint compensationprocess based on a compensation value, according to an exemplaryembodiment. Referring to FIG. 5, a distortion correction apparatus 510may assign viewpoints to pixels of a display panel 520, and may displaya first image on the display panel 520 based on source images thatcorrespond to the pixels of the display panel 520. FIG. 5 illustratessource images that correspond to respective viewpoints of the displaypanel 520 and the viewpoints of the display panel 520 on the firstimage. Numbers of the first image may indicate the viewpoints assignedto the pixels, and patterns of the first image may indicate colors thatcorrespond to the viewpoints.

The distortion correction apparatus 510 may output the first image via a3D optical apparatus 530, and a camera 540 may capture the display panel520 at a first point 550 while the first image is output via the 3Doptical apparatus 530. For example, a source image that corresponds to afirst viewpoint may be assumed to be observed at the first point 550when there is no distortion. The distortion correction apparatus 510 maygenerate a second image based on an image acquired by the camera 540.The second image may include source images that correspond to viewpointsother than the first viewpoint. Accordingly, the second image may bedetermined to be distorted.

The distortion correction apparatus 510 may determine a compensationvalue based on a difference between the second image and the sourceimage that corresponds to the first viewpoint. For example, thedistortion correction apparatus 510 may determine the compensation valuebased on Equation 5 described above. The distortion correction apparatus510 may update at least a portion of the viewpoints of the display panel520 based on the compensation value. The distortion correction apparatus510 may correct the second image by repeating the updating of the firstimage and updating of the compensation value based on the updated firstimage. When the distortion is corrected, the source image thatcorresponds to the first viewpoint may be observed from the correctedsecond image.

FIG. 6 is a diagram illustrating another example of a viewpointcompensation process based on a compensation value, according to anexemplary embodiment. A distortion correction apparatus 611 may assignviewpoints to pixels of a display panel 612, and may display a firstimage on the display panel 612 based on source images that correspond tothe pixels of the display panel 612. The distortion correction apparatus611 may output the first image via a 3D optical apparatus 613, andcameras 614 and 615 may capture the display panel 612 at a first point616 and a second point 617 while the first image is output via the 3Doptical apparatus 613. The distortion correction apparatus 611 maygenerate a second image and a third image based on images acquired bythe cameras 614 and 615. For example, it may be assumed that when thereis no distortion, a source image that corresponds to a first viewpointis observed at the first point 616 and a source image that correspondsto a second viewpoint is observed at the second point 617. Thedistortion correction apparatus 611 may determine a first compensationvalue based on a difference between a second image and the source imagethat corresponds to the first viewpoint, and may determine a secondcompensation value based on a difference between a third image and thesource image that corresponds to the second viewpoint. The distortioncorrection apparatus 611 may determine a compensation value based onEquation 5 as described above.

A distortion correction apparatus 621 may assign viewpoints to pixels ofa display panel 622, and may display a first image on the display panel622 based on source images that corresponds to the pixels of the displaypanel 622. The distortion correction apparatus 621 may output the firstimage via a 3D optical apparatus 623. The distortion correctionapparatus 611, the display panel 612 and the 3D optical apparatus 613may have the same configuration as the distortion correction apparatus621, the display panel 622 and the 3D optical apparatus 623,respectively, although the distortion correction apparatus 611, thedisplay panel 612 and the 3D optical apparatus 613 are separated fromthe distortion correction apparatus 621, the display panel 622 and the3D optical apparatus 623 as shown in FIG. 6.

The distortion correction apparatus 621 may track a position of a userby using a camera 624. For example, it may be assumed that the user islocated at a third point 629 and that a source image that corresponds toa third viewpoint is observed at the third point 629 when there is nodistortion. The distortion correction apparatus 621 may determine athird compensation value that is usable to compensate for a distortionobserved at the third point 629 based on the first compensation valueand the second compensation value. A fourth point 627 may correspond tothe first point 616 and a fifth point 628 may correspond to the secondpoint 617. For example, when the user is located at the fourth point627, the first compensation value may be applied to viewpoints of thedisplay panel 622. When the user is located at the fifth point 628, thesecond compensation value may be applied to the viewpoints of thedisplay panel 622. The distortion correction apparatus 621 may determinethe third compensation value based on a distance between the fourthpoint 627 and the fifth point 628 and a difference between the firstcompensation value and the second compensation value. For example, thedistortion correction apparatus 621 may determine the third compensationvalue based on a ratio between the distance between the fourth point 627and the fifth point 628 and the difference between the firstcompensation value and the second compensation value.

The distortion correction apparatus 621 may update at least a portion ofthe viewpoints of the display panel 622 based on the third compensationvalue. The distortion correction apparatus 621 may correct the secondimage by repeating the updating of the third image and then updating ofthe compensation value based on the updated third image. The distortionis corrected, and the source image that corresponds to the thirdviewpoint may be observed from the corrected second image. In theexample of FIG. 6, a distortion of an image associated with the thirdpoint 629 that is not determined in advance may be corrected. Inaddition, the distortion correction apparatus 510 of FIG. 5 does nothave a relevance to parameters of the 3D optical apparatuses 613 and623, and accordingly the example of FIG. 6 may be applicable to anexample in which the 3D optical apparatuses 613 and 623 have atypicalshapes.

FIG. 7 is a diagram illustrating a process of estimating a gap,according to an exemplary embodiment. Based on the above-describedcompensation value, a gap between a display panel and a 3D opticalapparatus may be estimated. When the gap between the display panel andthe 3D optical apparatus is not regular, an image may be distorted andfields of view (FOVs) may be different from each other for each of thepixels of the display panel. Accordingly, when a user is out of aposition to which a compensation value is applied, an appropriateadjustment value may need to be applied to viewpoints of the pixelsbased on different FOVs.

FIG. 7 illustrates a display panel 701, a position 702 of a 3D opticalapparatus in a design, and an estimated position 703 of the 3D opticalapparatus. In FIG. 7, d denotes a distance between the display panel 701and a camera 704, t denotes a gap in the design, h denotes a pitch inthe design, h′ denotes a pitch calculated based on a compensation value,and t′ denotes an estimated gap. For example, when a central point of aslit barrier or a slanted lens is at a position 721, the camera 704 mayshow a pixel at a position 711. When the 3D optical apparatus isactually located at the position 703, the camera 704 may show a pixel ata position 712 away from the position 711 by Δh. In this example, thepixel at the position 711 may not be shown because the pixel is coveredby a slit barrier or a slanted lens 732, and the pixel at the position712 may pass through a position 722 that is a central point of the slitbarrier or slanted lens. For example, when pitches, the sizes of theslit barrier or the slanted lens 731 and 732, of the 3D opticalapparatus are assumed to have the same size, sizes of the pitches h andh′ projected onto the display panel 701 may be proportional to the gapst and t′ between the display panel 701 and the 3D optical apparatus. Thepitch h′ may be obtained by using the following Equations:

$\begin{matrix}{g_{ij} = \frac{v_{i{({j + 1})}}^{c} - v_{i{({j - 1})}}^{c}}{2}} & \left\lbrack {{Equation}\mspace{14mu} 6} \right\rbrack\end{matrix}$

In Equation 6, g_(ij) denotes a horizontal variation of a viewdifference. Based on the variation g_(ij) and Equation 7, Δh may beobtained as shown in Equation 7 below.

$\begin{matrix}{{\Delta \; h} = {\frac{g_{ij}}{360}h}} & \left\lbrack {{Equation}\mspace{14mu} 7} \right\rbrack\end{matrix}$

In Equation 7, 360 denotes a range of hue values. As described above, acorresponding value may change based on a range of feature values of aused pattern. h may be obtained as shown in Equation 8 below.

$\begin{matrix}{h = {p\; \cos \; \alpha \frac{d}{d - t}}} & \left\lbrack {{Equation}\mspace{14mu} 8} \right\rbrack\end{matrix}$

In Equation 8, h denotes a horizontal size p cos α of a pitch projectedonto the display panel 701 in a design of an optical apparatus, pdenotes a pitch, d denotes a distance between the display panel 701 andthe camera 704, and t denotes a gap between the display panel 701 andthe 3D optical apparatus. When the gap t becomes closer to zero, h mayhave a value closer to p cos α. When the gap t increases, h mayincrease. Based on the above model, the gap t′ may be estimated asexpressed in Equation 9 below.

$\begin{matrix}{t^{\prime} = {d\left( {1 - \frac{p\; \cos \; \alpha}{h + {\Delta \; h}}} \right)}} & \left\lbrack {{Equation}\mspace{14mu} 9} \right\rbrack\end{matrix}$

When the gap t′ is obtained for all pixels of the display panel 701, ageometric model of the 3D optical apparatus may be determined based onthe gap t′. In addition, FOVs of all the pixels of the display panel 701may be determined based on the gap t′ or the geometric model of the 3Doptical apparatus, which will be further described with reference toFIG. 9 below.

FIG. 8 is a diagram illustrating a process of determining an adjustmentvalue, according to an exemplary embodiment. FIG. 8 illustrates pixels801 and 802 of a display panel, a position 811 of a 3D optical apparatusbased on a gap t′ estimated for the pixel 801, a position 812 of the 3Doptical apparatus based on a gap t′ estimated for the pixel 802, and apoint p₁ at which the camera 704 of FIG. 7 is located to acquire animage for obtaining a view difference, and a point p₂ at which a user islocated. When the gap t′ estimated for the pixel 801 is greater than thegap t′ estimated for the pixel 802 as shown in FIG. 8, an FOV of thepixel 802 may be greater than an FOV of the pixel 801. An FOV of a pixelu_(ij) of the display panel may be obtained by using Equation 10 shownbelow.

$\begin{matrix}{\varphi_{ij} = {\tan^{- 1}\left( \frac{p\; \cos \; \alpha}{2\; t_{ij}^{\prime}} \right)}} & \left\lbrack {{Equation}\mspace{14mu} 10} \right\rbrack\end{matrix}$

In Equation 10, ϕ_(ij) denotes the FOV of the pixel u_(ij), t_(ij)′denotes a gap for the pixel u_(ij). An angle ψ_(ij) between the pointp₁, the pixel u_(ij) and the point p₂ may be obtained by using Equation11 shown below.

$\begin{matrix}{\psi_{ij} = {\cos^{- 1}\left( \frac{\left( {p_{1} - u_{ij}} \right) \circ \left( {p_{2} - u_{ij}} \right)}{{{p_{1} - u_{ij}}}{{p_{2} - u_{ij}}}} \right)}} & \left\lbrack {{Equation}\mspace{14mu} 11} \right\rbrack\end{matrix}$

A variation in viewpoint numbers based on a movement of a position maybe determined based on an FOV of a corresponding pixel. For the samemovement distance, a variation in a viewpoint number of a pixel with anarrow FOV may increase, in comparison to a pixel with a wide FOV. Basedon the variation in the viewpoint number, an adjustment value may berepresented as expressed in Equation 12 below.

$\begin{matrix}{v_{ij}^{w} = \frac{\psi_{ij}}{\varphi_{ij}}} & \left\lbrack {{Equation}\mspace{14mu} 12} \right\rbrack\end{matrix}$

In Equation 12, v_(ij) ^(w) denotes an adjustment value that correspondsto an i-th row and j-the column. Referring to Equation 12, theadjustment value v_(ij) ^(w) may be determined by a ratio between theFOV ϕ_(ij) and the angle ψ_(ij). As described above, the distortioncorrection apparatus may generate an image that has a correcteddistortion by assigning viewpoint numbers to all pixels of the displaypanel based on Equation 1. In the example of FIG. 8, the distortioncorrection apparatus may assign viewpoint numbers that correspond to thepoint p₂ to all the pixels of the display panel based on an initialviewpoint number, a compensation value obtained at the point p₁ and anadjustment value for the point p₂. The distortion correction apparatusmay correct a distortion at the point p₂ based on a movement of the userin addition to the point p1 at which the compensation value iscalculated by the adjustment value.

FIG. 9 is a diagram illustrating a viewpoint adjustment process based onan adjustment value, according to an exemplary embodiment. Referring toFIG. 9, a distortion correction apparatus 911 may assign viewpoints topixels of a display panel 912, and may display a first image on thedisplay panel 912 based on source images that correspond to the pixelsof the display panel 912. The distortion correction apparatus 911 mayoutput the first image via a 3D optical apparatus 913. A camera 914 maycapture the display panel 912 at a first point 915 while the first imageis output via the 3D optical apparatus 913. The distortion correctionapparatus 911 may generate a second image based on an image acquired bythe camera 914. For example, it may be assumed that a source image thatcorresponds to a first viewpoint is observed at the first point 915 whenthere is no distortion. The distortion correction apparatus 911 maydetermine a first compensation value based on a difference between asecond image and the source image that corresponds to the firstviewpoint. The distortion correction apparatus 911 may determine acompensation value based on Equation 5 described above.

A distortion correction apparatus 921 may assign viewpoints to pixels ofa display panel 922, and may display a first image on the display panel922 based on source images that correspond to the pixels of the displaypanel 922. The distortion correction apparatus 921 may output the firstimage via a 3D optical apparatus 923. The distortion correctionapparatus 911, the display panel 912 and the 3D optical apparatus 913may have the same configuration as the distortion correction apparatus921, the display panel 922 and the 3D optical apparatus 923,respectively, although the distortion correction apparatus 911, thedisplay panel 912 and the 3D optical apparatus 913 are separated fromthe distortion correction apparatus 921, the display panel 922 and the3D optical apparatus 923 as shown in FIG. 9.

The distortion correction apparatus 921 may track a position of a userby using a camera 924. For example, it may be assumed that the user islocated at a second point 927 and that a source image that correspondsto a second viewpoint is observed at the second point 927 when there isno distortion. When viewpoints based on a compensation value thatcorresponds to the first point 915 is assigned to the pixels of thedisplay panel 922, a distortion may be observed at the second point 927,because respective FOVs may be different from each other for each of thepixels, as described above. The distortion correction apparatus 921 maydetermine an adjustment value that corresponds to the second point 927based on Equation 12. The distortion correction apparatus 921 may updateat least a subset of the viewpoints of the display panel 922 by applyingthe compensation value that corresponds to the first point 915 and theadjustment value that corresponds to the second point 927 to Equation 1.The distortion correction apparatus 921 may correct a distortion at apoint p2 based on a movement of a user in addition to a point 926 atwhich a compensation value is calculated by using an adjustment value inthe second point 927 that corresponds to the movement of the user.

FIG. 10 is a diagram illustrating a process of determining correspondingpoints for visible pixels, according to an exemplary embodiment.Referring to FIG. 10, a distortion correction apparatus may assignviewpoints to pixels of a display panel 1010, and the display panel 1010may display a first image based on source images that correspond to theassigned viewpoints. As described above, the source images may haverespective feature values that correspond to viewpoint numbers. Thedistortion correction apparatus may generate second images based onimages acquired by capturing the display panel 1010 at capturing pointsu1, u2 and u3 while the first image is output via a 3D opticalapparatus. For example, the distortion correction apparatus may generatea second image 1020 based on an image acquired by capturing the displaypanel 1010 at the capturing point u1. The second image 1020 may be animage converted to correspond to the first image, and the distortioncorrection apparatus may cut or rotate the image, in order to generatethe second image 1020.

The distortion correction apparatus may determine visible pixels for allrows of the second image 1020 and corresponding points for the visiblepixel, and may determine visible pixel lines based on the determinedcorresponding points. Hereinafter, a process of determining visiblepixel lines associated with a first row R1 of the second image 1020 willbe described. Similarly to the visible pixel lines associated with thefirst row R1, visible pixel lines associated with a second row R2 and athird row R3 of the second image 1020 may be determined.

The first row R1 may include pixels x1′, x2′, x3′ and x4′ whichrespectively correspond to pixels x1, x2, x3 and x4 of the first image.The distortion correction apparatus may determine pixels of the displaypanel 1010 that correspond to the pixels x1, x2, x3 and x4 as visiblepixels, based on a comparison between pixel values of the pixels x1, x2,x3 and x4 and pixel values of the pixels x1′, x2′, x3′ and x4′. Pixelvalues of the first image may be determined based on feature values, andaccordingly the distortion correction apparatus may compare featurevalues of the pixels x1, x2, x3 and x4 and feature values of the pixelsx1′, x2′, x3′ and x4′. The first image may be distorted due to aninfluence by the 3D optical apparatus when the first image is output,and accordingly a feature value of the pixel x1 may be different from afeature value of the pixel x1′. When a difference between the featurevalue of the pixel x1 and the feature value of the pixel x1′ is within apredetermined range, the distortion correction apparatus may determine apixel of the display panel 1010 that corresponds to the pixel x1 as avisible pixel. A process of determining visible pixels will be describedbelow.

When the display panel 1010 is on an x-y plane and when a capturingpoint or a viewing position is on a u-v plane, a four-dimensional (4D)light field of (x, y, u, v) may be defined. In the 4D light field, whenthe x-axis and the u-axis that are horizontal axes are taken intoconsideration, light entering from x to u may be displayed as a singlepoint on an x-u plane that is a 2D plane. In an example, when pixels ofthe display panel 1010 that correspond to the pixels x1, x2, x3 and x4are determined as visible pixels that are observed at the capturingpoint u1, visible pixels of the display panel 1010 may be displayed ascorresponding points 1035 on a 2D plane 1030. In another example, whenthe pixels of the display panel 1010 that correspond to the pixels x1,x2, x3 and x4 are determined as visible pixels that are observed at thecapturing points u1, u2 and u3, visible pixels of the display panel 1010may be displayed as corresponding points 1041, 1043 and 1045 on a 2Dplane 1040.

The distortion correction apparatus may connect the corresponding points1041, 1043 and 1045 and may determine visible pixel lines. Thecorresponding points 1041, 1043 and 1045 may indicate positions ofvisible pixels based on the capturing point u1. Accordingly, positionsof visible pixels based on an arbitrary viewing position may bespecified by visible pixel lines. The distortion correction apparatusmay analyze positions of visible pixels observed at an arbitrary viewingposition, and may assign a viewpoint that corresponds to the viewingposition to the visible pixels. In an example other than the example ofFIG. 10, at least three capturing points may be provided. In thisexample, a number of corresponding points may increase depending on anumber of capturing points. As described above, the corresponding points1041, 1043 and 1045 may be determined for the first row R1 of the secondimage 1020, and accordingly corresponding points may be determined forthe other rows of the second image 1020.

FIG. 11 is a diagram illustrating a relationship between a gap andvisible pixel lines, according to an exemplary embodiment. Referring toFIG. 11, a distortion correction apparatus may determine correspondingpoints for visible pixels on a 2D plane 1110, and may determine visiblepixel lines by connecting the corresponding points. A 3D opticalapparatus 1130 may include optical elements through which light of alimited direction propagates, for example, a slit of a parallax barrieror a curve of a lenticular lens. For example, light emitted from adisplay panel 1120 may reach a viewing position 1140 through the opticalelements of the 3D optical apparatus 1130.

Ax denotes a change in a position of a pixel that emits light to anoptical element 1135 on the display panel 1120, and Δu denotes a changein a position of a point at which light reaches from the optical element1135 on the viewing position 1140. A slope of a visible pixel line maybe determined based on Δx and Δu. The optical elements of the 3D opticalapparatus 1130 may be distorted, for example, bent, and accordinglyvisible pixel lines may have different respective slopes for each of theoptical elements.

In FIG. 11, t denotes a gap between the 3D optical apparatus 1130 and aviewing position 1140, and d denotes a distance between the displaypanel 1120 and the 3D optical apparatus 1130. A ratio between the gap tand the distance d may be equal to a ratio between the changes Δx andΔu. Accordingly, a slope a of a visible pixel line may be represented asexpressed in Equation 13 below, and the gap t may be represented basedon Equation 13 as expressed in Equation 14 below.

$\begin{matrix}{a = \frac{t}{d}} & \left\lbrack {{Equation}\mspace{14mu} 13} \right\rbrack \\{t = \frac{d\; \Delta \; u}{\Delta \; x}} & \left\lbrack {{Equation}\mspace{14mu} 14} \right\rbrack\end{matrix}$

Accordingly, the distortion correction apparatus may obtain the gap tbased on the slope a and the distance d. Equation 14 may be associatedwith the optical element 1135, however, there is no limitation thereto.For example, the distortion correction apparatus may obtain a gap forthe other optical elements using a similar scheme to the above-describedscheme.

FIG. 12 is a diagram illustrating visible pixel lines and a line,according to an exemplary embodiment. A distortion correction apparatusmay form visible pixel lines and may identify a visible pixel observedat a predetermined viewing position. For example, the distortioncorrection apparatus may determine intersection points between thevisible pixel lines and a line m that corresponds to a viewing positionU (not shown), and may determine pixels that correspond to theintersection points among pixels of a display panel as visible pixelsobserved at the viewing position U. The distortion correction apparatusmay reassign a viewpoint that corresponds to the viewing position U tothe pixels that correspond to the intersection points. For example, afirst pixel of the display panel that corresponds to an x-coordinate x1of an intersection point between the line m and a visible pixel line1210 may be determined as a visible pixel observed at the viewingposition U. Similarly, a second pixel, a third pixel and a fourth pixelof the display panel which respectively correspond to x-coordinates x2,x3 and xn of intersection points between the line m and visible pixellines 1220, 1230 and 1240 may be determined as visible pixels observedat the viewing position U. Accordingly, the distortion correctionapparatus may reassign the viewpoint that corresponds to the viewingposition U to the first pixel through the fourth pixel.

FIG. 13 is a diagram illustrating observation of feature values,according to an exemplary embodiment. A distortion correction apparatusmay determine a visible pixel based on x-coordinates of a display panel.Because source images may have respective feature values that correspondto viewpoint numbers as described above, the distortion correctionapparatus may determine x-coordinates based on feature values. Forexample, red that corresponds to a first viewpoint may be output from afirst pixel of the display panel. The distortion correction apparatusmay recognize coordinates of pixels of the display panel. For example,an x-coordinate of the first pixel may be x1. In this example, when redis observed at a second pixel of a second image, the distortioncorrection apparatus may determine the first pixel as a visible pixeland may determine an x-coordinate of a corresponding point for thevisible pixel to be x1.

Despite the same pixels of the display panel, different x-coordinatesmay be determined based on feature values observed in the second image.The above difference may be caused by an offset of an optical element.For example, feature values based on hue values may be assigned to thepixels of the display panel, and an i-th pixel of the display panel maybe observed at a capturing point u1. In an example, when green G isobserved at the i-th pixel through a ray 1310, the distortion correctionapparatus may determine a position of the i-th pixel based on anx-coordinate that corresponds to green G. In another example, when blueB is observed at the i-th pixel through a ray 1320, the distortioncorrection apparatus may determine a position of the i-th pixel based onan x-coordinate that corresponds to blue B.

FIG. 14 is a diagram illustrating a process of determining a visiblepixel, according to an exemplary embodiment. As described above, while afirst image displayed on a display panel is output via a 3D opticalapparatus 1420, a distortion correction apparatus may generate a secondimage by capturing the display panel, and may determine a visible pixelbased on pixel values of pixels included in the second image. Forexample, the 3D optical apparatus 1420 may interfere with light outputfrom pixels of the display panel. Because the distortion correctionapparatus may estimate a position of a visible pixel based on the pixelvalues of the pixels in the second image, an error may occur in theposition of the visible pixel when an error is included in the pixelvalues. Accordingly, the distortion correction apparatus may determinethe visible pixel by executing a verification of the pixel values of thepixels in the second image. For example, the distortion correctionapparatus may compare a pixel value actually assigned to the displaypanel to a pixel value observed via the second image. In this example,when a difference between the pixel values is within a predeterminedvisible range, a pixel of the display panel as a visible pixel.

FIG. 14 illustrates a first row 1410 of the first image and a first row1430 of the second image. The distortion correction apparatus maygenerate the second image by capturing the display panel at a capturingpoint u while the first image is output via the 3D optical apparatus1420. A feature value of a first pixel included in the first row 1410may be red R, and a feature value of a second pixel included in thefirst row 1410 may be orange O. Also, a feature value of a first pixelincluded in the first row 1430 may be red R, and a feature value of asecond pixel included in the first row 1430 may be blue B. A visiblerange 1405 may be determined based on an optical element. For example,the visible range 1405 may be determined based on a width of a lens,because feature values by light output from pixels adjacent to a lensmay be observed at the lens.

The feature value, that is, red R of the first pixel in the first row1430, is within the visible range 1405 from the feature value of thefirst pixel in the first row 1410, and accordingly the distortioncorrection apparatus may determine a pixel of the display panel thatcorresponds to the first pixel in the first row 1410 as a visible pixel.In addition, the feature value, that is, blue B of the second pixel inthe first row 1430, is out of the visible range 1405 from the featurevalue of the second pixel in the first row 1410, and accordingly thedistortion correction apparatus may exclude a pixel of the display panelthat corresponds to the second pixel in the first row 1410 from visiblepixels. When visible pixels are determined as described above, thedistortion correction apparatus may display corresponding points for thevisible pixels on a 2D plane 1435.

FIG. 15 is a diagram illustrating correction of a head-up display (HUD)image, according to an exemplary embodiment. FIG. 15 illustrates aglasses-free 3D display apparatus 1510, mirrors 1520 and 1530, and aglass 1540 (such as, for example, a windshield) of a vehicle. A user mayobserve an image displayed on the glasses-free 3D display apparatus 1510through the glass 1540. Generally, the glass 1540 may have an atypicalshape. Exemplary embodiments may be applicable to an atypical shape of adisplay, and accordingly may also be applicable to a HUD that uses theglass 1540. In an example, when a user is assumed to observe an image ata fixed point 1550, viewpoints of the 3D display apparatus 1510 may bedetermined based on a single compensation value that is calculated forthe point 1550 in advance. In another example, when the user is assumedto observe an image at another point, a position of the user or aposition of the eye of the user may be tracked, a compensation valuethat corresponds to the tracked position may be determined based on atleast two compensation values calculated in advance, and viewpoints ofthe 3D display apparatus 1510 may be determined based on the determinedcompensation value.

FIG. 16 is a diagram illustrating correction of an image of smartglasses, according to an exemplary embodiment. FIG. 16 illustrates aglasses-free 3D display apparatus 1610, mirrors 1620 and 1630, and alens 1640 of the smart glasses. A user may observe an image displayed onthe glasses-free 3D display apparatus 1610 through the lens 1640.Generally, the lens 1640 may have an atypical shape. Exemplaryembodiments may be applicable to an atypical shape of a display asdescribed above, and accordingly may also be applicable to the lens1640. In the same scheme as described in FIG. 15, when a user is assumedto observe an image at a fixed point 1650, viewpoints of the 3D displayapparatus 1610 may be determined based on a single compensation valuethat is calculated for the point 1650 in advance. When the user isassumed to observe an image at another point, a position of the user ora position of the eye of the user may be tracked, a compensation valuethat corresponds to the tracked position may be determined based on atleast two compensation values calculated in advance, and viewpoints ofthe 3D display apparatus 1610 may be determined based on the determinedcompensation values.

FIG. 17 is a block diagram illustrating a distortion correctionapparatus, according to an exemplary embodiment. Referring to FIG. 17,the distortion correction apparatus includes a sensor 1710, a processor1720, and a memory 1730. The distortion correction apparatus mayselectively include the sensor 1710. The sensor 1710, the processor 1720and the memory 1730 may communicate via a bus 1740. The sensor 1710 mayinclude, for example, an image sensor or a depth sensor configured tocapture a display panel or track a position of a user. The sensor 1710may correspond to at least one of the above-described cameras. Thememory 1730 may include, for example, a nonvolatile memory such as ahard disk drive (HDD), a solid state drive (SSD) or a flash memory, or avolatile memory such as a dynamic random access memory (DRAM). Thememory 1730 may be a cache memory in the processor 1720. The memory 1730may include a computer-readable instruction. The instruction may be usedto perform the above-described operations. For example, when theinstruction is executed by the processor 1720, the processor 1720 mayassign viewpoints to pixels of a display panel, may display a firstimage on the display panel based on source images that correspond to theviewpoints, may generate a second image based on an image acquired bycapturing the display panel at a first point while the first image isoutput via a 3D optical apparatus, may determine a first compensationvalue that is usable to compensate for a distortion of the second imagedue to a geometric distortion between the display panel and the 3Doptical apparatus, and may update at least one of the viewpoints basedon the first compensation value. The above description is alsoapplicable to the distortion correction apparatus, and accordingly isnot repeated here.

FIG. 18 is a flowchart illustrating an example of a distortioncorrection method, according to an exemplary embodiment. Referring toFIG. 18, in operation 1810, a distortion correction apparatus may assignviewpoints to pixels of a display panel. In operation 1820, thedistortion correction apparatus may display a first image on the displaypanel based on source images that correspond to the viewpoints. Inoperation 1830, the distortion correction apparatus may generate asecond image based on an image acquired by capturing the display panelat a first point while the first image is output via a 3D opticalapparatus. In operation 1840, the distortion correction apparatus maydetermine a first compensation value that is usable to compensate for adistortion of the second image due to a geometric distortion between thedisplay panel and the 3D optical apparatus. In operation 1850, thedistortion correction apparatus may update at least a subset of theviewpoints based on the first compensation value. The above descriptionis also applicable to the distortion correction method, and accordinglyis not repeated here.

FIG. 19 is a flowchart illustrating another example of a distortioncorrection method, according to an exemplary embodiment. Referring toFIG. 19, in operation 1910, a distortion correction apparatus may assignviewpoints to pixels of a display panel. In operation 1920, thedistortion correction apparatus may display a first image on the displaypanel based on source images that correspond to the viewpoints. Inoperation 1930, the distortion correction apparatus may generate asecond image and a third image based on images acquired by capturing thedisplay panel at a first point and a second point while the first imageis output via a 3D optical apparatus. In operation 1940, the distortioncorrection apparatus may determine a first compensation value that isusable to compensate for a distortion of the second image and a secondcompensation value that is usable to compensate for a distortion of thethird image. In operation 1950, the distortion correction apparatus maydetermine a third compensation value based on the first compensationvalue and the second compensation value. The third compensation valuemay be used to compensate for a distortion observed at a third point. Inoperation 1960, the distortion correction apparatus may update at leasta subset of the viewpoints based on the third compensation value. Theabove description is also applicable to the distortion correctionmethod, and accordingly is not repeated here.

The exemplary embodiments described herein may be implemented usinghardware components, software components, or a combination thereof. Aprocessing device may be implemented using one or more general-purposeor special purpose computers, such as, for example, a processor, acontroller and an arithmetic logic unit, a digital signal processor, amicrocomputer, a field programmable array, a programmable logic unit, amicroprocessor or any other device capable of responding to andexecuting instructions in a defined manner. The processing device mayrun an operating system (OS) and one or more software applications thatrun on the OS. The processing device also may access, store, manipulate,process, and create data in response to execution of the software. Forpurpose of simplicity, the description of a processing device is used assingular; however, a person having ordinary skill in the art willappreciate that a processing device may include multiple processingelements and multiple types of processing elements. For example, aprocessing device may include multiple processors or a processor and acontroller. In addition, different processing configurations arepossible, such as parallel processors.

The software may include a computer program, a piece of code, aninstruction, or some combination thereof, to independently orcollectively instruct or configure the processing device to operate asdesired. Software and data may be embodied permanently or temporarily inany type of machine, component, physical or virtual equipment, computerstorage medium or device, or in a propagated signal wave capable ofproviding instructions or data to or being interpreted by the processingdevice. The software also may be distributed over network coupledcomputer systems so that the software is stored and executed in adistributed fashion. The software and data may be stored by one or morenon-transitory computer readable recording mediums.

The method according to the above-described exemplary embodiments may berecorded in non-transitory computer-readable media that include programinstructions to implement various operations which may be performed by acomputer. The media may also include, alone or in combination with theprogram instructions, data files, data structures, and the like. Theprogram instructions recorded on the media may be those speciallydesigned and constructed for the purposes of the exemplary embodiments,or they may be of the well-known kind and available to those havingskill in the computer software arts. Examples of non-transitorycomputer-readable media include magnetic media such as hard disks,floppy disks, and magnetic tape; optical media such as compact diskread-only memory (CD ROM) discs and digital versatile disks (DVDs);magneto-optical media such as optical discs; and hardware devices thatare specially configured to store and perform program instructions, suchas read-only memory (ROM), random access memory (RAM), flash memory, andthe like. Examples of program instructions include both machine code,such as code produced by a compiler, and files containing higher levelcode that may be executed by the computer using an interpreter. Thedescribed hardware devices may be configured to act as one or moresoftware modules in order to perform the operations of theabove-described exemplary embodiments, or vice versa.

While this disclosure includes exemplary embodiments, it will beapparent to one of ordinary skill in the art that various changes inform and details may be made in these exemplary embodiments withoutdeparting from the spirit and scope of the claims and their equivalents.The exemplary embodiments described herein are to be considered in adescriptive sense only, and not for purposes of limitation. Descriptionsof features or aspects in each example are to be considered as beingapplicable to similar features or aspects in other examples. Suitableresults may be achieved if the described techniques are performed in adifferent order, and/or if components in a described system,architecture, device, or circuit are combined in a different mannerand/or replaced or supplemented by other components or theirequivalents. Therefore, the scope of the disclosure is defined not bythe detailed description, but by the claims and their equivalents, andall variations within the scope of the claims and their equivalents areto be construed as being included in the present disclosure.

What is claimed is:
 1. A distortion correction method comprising:assigning viewpoints to pixels of a display panel; displaying a firstimage on the display panel based on source images that correspond to theviewpoints; generating a second image based on an image acquired bycapturing the display panel at a first point while the first image isoutput via a three-dimensional (3D) optical apparatus; determining afirst compensation value that is usable to compensate for a distortionof the second image due to a geometric distortion between the displaypanel and the 3D optical apparatus; and updating at least one of theviewpoints based on the first compensation value.
 2. The distortioncorrection method of claim 1, wherein the determining of the firstcompensation value comprises determining the first compensation valuebased on a difference between the second image and a source image thatcorresponds to a viewpoint of the first point.
 3. The distortioncorrection method of claim 1, further comprising: determining areference source image observed at a reference point in the secondimage, wherein the determining of the first compensation value comprisesdetermining the first compensation value so that the reference sourceimage is displayed on an entire area of the second image.
 4. Thedistortion correction method of claim 3, wherein each of the sourceimages has a respective feature value that corresponds to a viewpointnumber, and the determining of the first compensation value comprisesdetermining the first compensation value based on a difference between afeature value of the reference source image and at least one featurevalue of a different source image.
 5. The distortion correction methodof claim 1, wherein each of the source images has a respective featurevalue that is determined based on hue values that are at regularintervals or intensity values that are at regular intervals.
 6. Thedistortion correction method of claim 1, further comprising: determininga second compensation value based on a third image generated bycapturing the display panel at a second point, the second compensationvalue being usable to compensate for a distortion of the third image;and determining a third compensation value based on the firstcompensation value and the second compensation value, the thirdcompensation value being usable to compensate for a distortion observedat a third point, wherein the updating of at least one of the viewpointscomprises updating at least one of the viewpoints based on the thirdcompensation value.
 7. The distortion correction method of claim 6,wherein the third compensation value is determined based on a distancebetween the first point and the second point and a difference betweenthe first compensation value and the second compensation value.
 8. Thedistortion correction method of claim 6, further comprising: detectingan eye position of a user of the display panel; and determining thethird point based on the detected eye position.
 9. The distortioncorrection method of claim 1, further comprising: determining respectivefields of view (FOVs) for each of the pixels based on a geometric modelof the 3D optical apparatus; determining respective angles formed by thefirst point, each of the pixels, and a fourth point that is differentfrom the first point; determining an adjustment value based on thedetermined FOVs and the determined angles, the adjustment value beingusable to compensate for a distortion observed at the fourth point; andupdating at least one of the viewpoints based on the determinedadjustment value.
 10. The distortion correction method of claim 9,wherein the geometric model is determined based on a gap between thedisplay panel and the 3D optical apparatus, and the gap is estimatedbased on the first compensation value.
 11. The distortion correctionmethod of claim 9, wherein the adjustment value is determined based on aratio between the determined FOVs and the determined angles.
 12. Adistortion correction method comprising: assigning viewpoints to pixelsof a display panel; displaying a first image on the display panel basedon source images that correspond to the viewpoints; generating a secondimage and a third image based on respective images acquired by capturingthe display panel at a first point and a second point while the firstimage is output via a three-dimensional (3D) optical apparatus;determining a first compensation value that is usable to compensate fora distortion of the second image and a second compensation value that isusable to compensate for a distortion of the third image; determining athird compensation value based on the first compensation value and thesecond compensation value, the third compensation value being usable tocompensate for a distortion observed at a third point; and updating atleast one of the viewpoints based on the third compensation value. 13.The distortion correction method of claim 12, wherein the determining ofthe first compensation value and the second compensation value comprisesdetermining the first compensation value based on a difference betweenthe second image and a source image that corresponds to a viewpoint ofthe first point.
 14. The distortion correction method of claim 12,further comprising: determining a reference source image observed at areference point in the second image, wherein the determining of thefirst compensation value and the second compensation value comprisesdetermining the first compensation value so that the reference sourceimage is displayed on an entire area of the second image.
 15. Thedistortion correction method of claim 14, wherein each of the sourceimages has a respective feature value that corresponds to a viewpointnumber, and the determining of the first compensation value and thesecond compensation value comprises determining the first compensationvalue based on a difference between a feature value of the referencesource image and at least one feature value of a different source image.16. The distortion correction method of claim 12, wherein the thirdcompensation value is determined based on a distance between the firstpoint and the second point and a difference between the firstcompensation value and the second compensation value.
 17. A distortioncorrection method comprising: assigning viewpoints to pixels of adisplay panel; displaying a first image on the display panel based onsource images that correspond to the viewpoints; generating secondimages based on respective images acquired by capturing the displaypanel at corresponding capturing points while the first image is outputvia a three-dimensional (3D) optical apparatus; determining, based onthe generated second images, visible pixel lines associated with visiblepixels of the display panel observed at the capturing points;determining intersection points between the visible pixel lines and aline that corresponds to a viewing position; and reassigning a viewpointthat corresponds to the viewing position to pixels that correspond tothe determined intersection points among the pixels of the displaypanel.
 18. The distortion correction method of claim 17, wherein thedetermining of the visible pixel lines comprises: determiningcorresponding points for the visible pixels based on respective pixelvalues of the generated second images, the corresponding pointsrepresenting respective positions of the visible pixels based on thecapturing points; and determining the visible pixel lines by connectingthe determined corresponding points.
 19. The distortion correctionmethod of claim 18, wherein each of the source images has a respectivefeature value that corresponds to a viewpoint number, and thedetermining of the corresponding points comprises: determining a pixelof the display panel that corresponds to a first pixel included in thefirst image as a visible pixel, based on a comparison between a featurevalue of the first pixel and a feature value of a second pixel thatcorresponds to the first pixel among pixels included in the generatedsecond images; and determining a corresponding point for the visiblepixel based on the feature value of the second pixel.
 20. Anon-transitory computer-readable storage medium storing a program forcausing a processor to perform the method of claim 1.